Statistics: Mean, Median, Mode, and Range

To find the median, arrange all ages in ascending order: 7, 9, 12, 13, 16. With 5 values (odd number), the median is the middle (3rd) value, which is 12.

The mode is the value that appears most frequently in the data set. Counting frequencies: 8(1), 11(1), 9(3), 14(1), 15(1), 18(1), 6(1), 10(1). The number 9 appears 3 times, more than any other value.

Old mean = 35
New mean = 35 + 21 = 56
So, the mean increases.

Mean is calculated by summing all values and dividing by the count. Sum = 157.5 + 152.5 + 165.7 + 151.3 + 160.6 + 156.4 = 944.0. Mean = 944.0 ÷ 6 = 157.3 (rounded to one decimal place).

Total value of all 5 items = mean × number of items = £7 × 5 = £35. Sum of first four items = £6.50 + £8 + £5.50 + £6 = £26. Therefore, fifth item = £35 - £26 = £9.

The first 10 whole numbers are 0, 1, 2, 3, 4, 5, 6, 7, 8, 9. Their sum = 45. Mean = 45 ÷ 10 = 4.5. Remember that whole numbers start from 0, not 1.

Sum of all 5 quantities = 5 × 6 = 30. Sum of 3 quantities = 3 × 8 = 24. Sum of remaining 2 quantities = 30 - 24 = 6. Average of remaining 2 = 6 ÷ 2 = 3.

The mode is defined as the value that occurs most frequently. In this data set (7, 5, 56, 89, 75, 45), every number appears exactly once. Since no value repeats, there is no mode.

Range = maximum value - minimum value. From the data set 2, 15, 3, 3, 25, 17, the maximum is 25 and minimum is 2. Range = 25 - 2 = 23.

Range is calculated as maximum minus minimum. From the data 8, 9, 6, 4, 9, 9, 9, 15, 5, 4, we have maximum = 15 and minimum = 4. Range = 15 - 4 = 11.

Range is the difference between maximum and minimum values. Maximum = 10, minimum = 3, so range = 10 - 3 = 7. This measures how spread out the data is.

Mode is the value that appears most frequently. T appears 4 times, P appears 2 times, Q appears 3 times. Since T has the highest frequency (4), it is the mode.

Mean = sum of all values divided by count. Sum = 11+13+15+9+11+21+11 = 91. Count = 7. Mean = 91 ÷ 7 = 13. Option A is correct.

Mean = sum ÷ count. Sum = 22+25+29+22+25+25+22+38 = 208. Count = 8. Mean = 208 ÷ 8 = 26. Option B is correct.

Median is the middle value when data is arranged in order. Sorted: 1, 2, 5, 7, 9, 12, 15, 20, 33, 55, 56. With 11 values, the 6th value (12) is the median.

Mean = total eggs sold ÷ number of days. Total = 11+9+9+11+11+8+9+20 = 88. Days = 8. Mean = 88 ÷ 8 = 11 eggs per day. Option A is correct.

To find the mean, add all values and divide by the count. Sum = 19 + 18 + 29 + 20 + 18 + 14 + 23 = 141. Count = 7 students. Mean = 141/7 = 20.14.

The median is the middle value when data is arranged in order. Sorted values: 6, 8, 9, 18, 24. With 5 values, the median is the 3rd value, which is 9.

Range is the difference between the maximum and minimum values. Maximum = 12, Minimum = 3. Range = 12 - 3 = 9.

Mode = 10, as 10 is the most common value, repeating 3 times.

If the mean of 5 values is 21, then total sum = 21 × 5 = 105. Sum of four given values = 12 + 29 + 32 + 18 = 91. Fifth value = 105 - 91 = 14.

Mean = Sum of values / Count. Sum = 28 + 14 + 39 + 42 + 27 = 150. Count = 5. Mean = 150/5 = 30.

To achieve average 44 across 5 tests, total needed = 44 × 5 = 220. Current sum = 49 + 48 + 42 + 39 = 178. Required score = 220 - 178 = 42.